A, B, C, D and E are five towns out of which two are hill stations and the rest are in plain. Two towns, which are in plain, are harbours. Four towns out of five are capitals and two are industrial towns. Population of two towns is less than 5 lacs. It is 20 lacs of one town and more than 50lacs of two towns. Two towns are on the same latitudes and other two are on the same longitudes. Latitudes and longitudes of both harbours are different and out of these one is an industrial town. The population of both industrial towns is more than 50 lacs. The longitudes of one hill station and one of the industrial towns are same. The latitudes and longitudes of the other hill station and other harbour are different. One industrial town is neither a hill station nor a harbour. None of the hill stations is an industrial town. The hill station of which longitudes of A and E are same. E is a harbour. The latitudes of D and C are same and the population of D is 20 lacs. Both the harbours are capitals and one of them is an industrial town.
Which of the following two towns are those whose population is less than 5 lacs ?
We analyse the given information as follows :
Two are hill station.
Three are plains of which two are harbours.
Four towns are capitals.
Two towns are industrial.
Two towns have population less than 5 lacs.
One town has population 20 lacs.
Two towns have population more than 50 lacs.
Two towns are on same latitudes.
B is a hill station. E is a harbour. Clearly, A which has the same longitude as E, cannot be a harbour and clearly, D having population 20 lacs cannot be an industrial town. So, it is a harbour. Thus, E and D are harbours.
Clearly, one harbour is industrial town but D is not. So, E is an industrial town with population more than 50 lacs. Clearly, longitudes of a hill station and industrial town are same. So, A having same longitude as E, is a hill station. Latitudes of D and C are same and D is harbour. So, C cannot be a hill station. So, B is the other hill station. Thus, three plains are C, D, E. One industrial town is neither a hill station nor a harbour. So, C is an industrial town with population more than 50 lacs. Clearly, both harbours are capitals. So, E and D are capitals. The hill station A, having same longitude as a harbour, is also a capital. Population of D is 20 lacs. So, population of A and B is less than 5 lacs. Clearly, only one hill station is capital. So, C is the other capital.
Clearly, population of A and B is less than 5 lacs.